Study On The Tidal And Non-tidal Variation Of Earth’s Rotation

The study of Earth’s rotation variation is the basis of space navigation,precise satellite orbit determination,time scale and space reference frame connection.The Earth rotation refers to the motion of its reference axis(pole)with respect to the Earth’s body which characterized by polar motion and rotation velocity variation,and the motion with respect to the inertial space which characterized by precession-nutation.The mechanical mechanism of the Earth rotation mainly include: the gravitation of the external celestial bodies(mainly the Sun and the Moon);the material migration on the Earth’s surface and inside;the various load variations on the Earth’s surface.Associated Legendre polynomials and vector spherical functions are the basic mathematical tools for the study of Earth gravitational potential and crustal deformation.In this study,these mathematical tools are studied theoretically,and the basic concepts of the Earth’s gravitational potential and tide are briefly introduced.Then,on the basis of further improving the dynamic and kinematic theory of the Earth rotation,the tidal and non-tidal variations of the Earth’s rotation are studied in detail.The main works are as follows:Improvement of recursive formula of associated Legendre polynomials.In this part,the general recursive algorithms are studied firstly,a defect in Belikov(1991)is pointed out and the correction is given.A super cross order recursive algorithm is proposed in this study,and the related calculation is carried out.Then,the description of the complex spherical vector function is improved.At the end of this part,the expressions of the displacement field,strain tensor field are deduced,and the definitions of the tidal deformation displacement and Earth’s figure axis are given.Study of the tidal effects in spatial geodesy.In the research of tidal potential generating development,some defects in previous studies are pointed out,the six order Laplace tidal potential generating development and the torque expressions of precession-nutation are given.Then,the influence of the Love number frequency characteristics on the Earth’s gravity field and station displacement are recalculated.It is pointed out that the influence of polar motion and Earth’s rotation rate on gravity observation and vertical deviation should be considered in modern high-precision space geodesy.Further study on the dynamic theory of Earth rotation with liquid core.Firstly,a geometric theorem of the Earth rotation kinematics is established.The theoretical transformation relationship between the polar motion and precession-nutation of an arbitrary celestial reference axis and the polar motion and precession-nutation of the Earth’s rotation axis is given,and its correctness and convenience are proved.The dynamic equations of the triaxial Earth rotation with liquid core is re-deduced,and its excitation functions are studied in depth,the final expression of the excitation functions are given which are convenient for calculation and application.Study of the tidal variation of Earth rotation.The most salient feature of the Earth’s rotation is the tidal variation caused by the tidal generating force of the Sun and the Moon.Based on the above theoretical researches,the value of the scale factor is discussed in detail,combined with the latest tidal generating potential development,a new tidal variation sequence of the Earth’s rotation considering the atmospheric effect and mantle anelasticity is given.Compared with IERS(2010)and other related studies,the results show that the variations of the main periodic terms are relatively consistent.Study of the non-tidal variation of Earth’s rotation.The non-tidal influence on the variation of the Earth’s rotation is studied.The calculation result shows that there are about 23.8% of the long-term variations of the Earth’s rotation rate caused by the non-tidal effect.Then,the influence of global continental water storage on the Earth rotation is calculated,the results show that the induced excitation for prograde component of annual polar motion from land water storage is about 16.85 mas,and for annual component of LOD is about 44μs.The combination of atmospheric excitation and water storage excitation could well explain the difference between theory and observation,and there are still orther unknown excitation sources exist,the magnitude is about 10 mas.Finally,other non-tidal factors and their influence mechanism on the Earth’s rotation are discussed.The study shows that the Solar activity and crustal rebound after the last ice age are the orther important non-tidal factors,and there are also other non-tidal factors need to be further discussed.